9 votes

What exactly is the unique union of a family of sets?

The uniqueness is in the formula used to define the "unique union": $\{x \mid ∃!A(A∈F \land x∈A) \}$. This means that if an element $a$ belongs to e.g. two sets $A_1$ and $A_2$ of the ...
Mauro ALLEGRANZA's user avatar
3 votes

Un-definability of graphs with bounded out-degree

here is the compactness argument @Noah alludes to. Suppose for contradiction that bounded out degree is definable by some P. Then consider the following for each n: $d_n: \exists x_1,...,x_n [\...
emesupap's user avatar
  • 491
1 vote

Example of a sentence of the language $\{+,0,S\}$, unprovable in Q1--Q5 but provable in Q?

I can't solve the original problem yet. The best I can do is come up with a statement that's a theorem of the reduced theory of Robinson arithmetic plus a fictitious Q8 (shown below) but not of Q1-Q5. ...

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